Problem: Solve for $x$ and $y$ using elimination. ${-3x-2y = -28}$ ${-2x-2y = -24}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $-1$ ${-3x-2y = -28}$ $2x+2y = 24$ Add the top and bottom equations together. $-x = -4$ $\dfrac{-x}{{-1}} = \dfrac{-4}{{-1}}$ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {-3x-2y = -28}\thinspace$ to find $y$ ${-3}{(4)}{ - 2y = -28}$ $-12-2y = -28$ $-12{+12} - 2y = -28{+12}$ $-2y = -16$ $\dfrac{-2y}{{-2}} = \dfrac{-16}{{-2}}$ ${y = 8}$ You can also plug ${x = 4}$ into $\thinspace {-2x-2y = -24}\thinspace$ and get the same answer for $y$ : ${-2}{(4)}{ - 2y = -24}$ ${y = 8}$